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--- blog:2024-09-11-quiver-hecke-algebra [2024/09/11 18:45] – created pzhou
+++ blog:2024-09-11-quiver-hecke-algebra [2024/09/11 19:56] (current) – pzhou
@@ Line 12: / Line 12: @@
 So far, we have ignored the arrows. Let $E_V = \prod_{e \in E} Hom(V_{s(e)}, V_{t(e)})$. For any $x \in E_V$, and any (homogenous?) flag $\phi \in F(V)$, we say $x$ preserves $\phi$, if for each step $V^l_\phi$ in the flag $V_\phi^*$, $x$ restricts to a sub quiver rep on $V_\phi^l$.
+If the flag $V_\phi$ increase dimension one at a time, we call it a (graded?) full flag variety of $V$; otherwise a graded partial flag variety. Fix a flag type $\vec \nu$, consider all such pairs $\wt F_{\vec \nu} = \{(\phi, x)\}$. It project to $F_{\vec \nu} = \{\phi\}$, and also to $E_V = \{x\}$. The associated graded $V_\phi^l / V_\phi^{l-1}$ defines a collection of line bundles over $F_{\vec \nu}$ and pullback to $\wt F$.